* turn the compass needle so it is approximately parallel to the wire. * close the switch to send...
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* Turn the compass needle so it is approximately parallel to the wire. * Close the switch to send the current through the wire for about 5-10 seconds. * The compass will align itself with the magnetic field.
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B
Ampere’s circuital lawright hand rule
a
I
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current ==> magnetic field
74 10o Henries B jo
B ds j dso
B dl j dso
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concentric hollow cylinders
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0 100 200 300 400-5
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solenoid
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we know that • B = 0vector potential A
we know that • [ x vector] = 0
we can now specify the vectorlet vector be A such that B = x A
William Thomson shows that Neumann's
electromagnetic potential A is in fact the
vector potential from which may be
obtained via B = x A.
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vector potential A
we also know x B = µo j
B = x A
x x A = • A) -
- A = - µo j is similar to Poisson’s
equation but we have to solve three PDE’s
A and j are in the same direction!!
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summary
js
Three techniques to find B
1] Ampere’s circuital law - lots of symmetry
2] find vector potential A, then B = x A
3] Biot - Savart law
B
A
BB
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